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Question
N(3, −4) is the foot of the perpendicular drawn from the origin to line L. Find the equation of line L.
Solution
Slope of ON = `(-4 - 0)/(3 - 0) = (-4)/3`
Since line L ⊥ ON,
slope of the line L is `3/4` and it passes through point N(3, – 4).
Equation of the line in slope point form is
y – y1 = m(x – x1)
∴ Equation of line L is
y – (– 4) = `3/4(x - 3)`
∴ 4(y + 4) = 3(x – 3)
∴ 4y + 16 = 3x – 9
∴ 3x – 4y – 9 – 16 = 0
∴ 3x – 4y – 25 = 0
∴ 3x – 4y = 25
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